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| Paper IPM / Computer Science / 10832 |
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We consider an incremental optimal label placement in a closed-2PM map con-taining points each attached with a label. Labels are assumed to be axis-parallel square-shaped and have to be pairwise disjoint with maximum possible length each attached to its corresponding point on one of its horizontal edges. Such a labeling is denoted as optimal labeling. Our goal is to efficiently generate a new optimal labeling for all points after each new point being inserted in the map. Inserting each point may require several labels to flip or all labels to shrink. We present an algo-rithm that generates each new optimal labeling in O(lg n + k) time where k is the number of required label flips, if there is no need to shrink the label lengths, or in O(n) time when we have to shrink the labels and flip some of them. The algorithm uses O(n) space in both cases. This is a new result on this problem. Key words: computational geometry, map labeling, label updating * Corresponding author.
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